Internal problem ID [6104]
Internal file name [OUTPUT/5352_Sunday_June_05_2022_03_35_08_PM_97644046/index.tex]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 6. Existence and uniqueness of solutions to systems and nth order equations.
Page 254
Problem number: 2.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )+x y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=y_{2} \left (x \right )+x^{3} y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=2 x y_{2} \left (x \right )-y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right ) \end {align*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✗ Solution by Maple
dsolve([diff(y__1(x),x)=3*y__1(x)+x*y__3(x),diff(y__2(x),x)=y__2(x)+x^3*y__3(x),diff(y__3(x),x)=2*x*y__2(x)-y__2(x)+exp(x)*y__3(x)],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y1'[x]==3*y1[x]+x*y3[x],y2'[x]==y2[x]+x^3*y3[x],y3'[x]==2*x*y1[x]-y2[x]+Exp[x]*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
Not solved